Equations as Relations By: Cathy Miller Bartlett High School Lesson for Glencoe Algebra I Math...

Equations as RelationsBy: Cathy Miller

Bartlett High School

Lesson for Glencoe Algebra I Math

Section 4-4

Algebra I Glencoe Mathematics 2004

The McGraw Hill Companies Inc.

Ways to write a relation

• Set of ordered pairs

• Table

• Mapping

• Graph

• Equation in two variables

New VocabularyEquation in Two Variables – Equations with 2 different variables.

Solution to Equation in Two Variables – any point that makes a true statement when you substitute the x and y values into the equation.

Solve Using a Replacement SetReplacement set = a set of possible solutions.

Substitute the points to find the true solutions… these are the ones that make the equation true.

Solution set = the set of true solutions.

Solve -3x+y=7 if the replacement set is {(-5,0),(-3,-2),(2,13),(4,19)}

x y -3x+y=7-5 0 -3 -2

-3(-5)+(0)=7 15 = 7-3(-3)+(-2)=7 7=7

Solve -3x+y=7 if the replacement set is {(-5,0),(-3,-2),(2,13),(4,19)}

x y -3x+y=7 2 13 4 19

-3(2)+(13)=7 7=7-3(4)+(19)=7 7=7

Solve y=7+3x if the replacement set is {(-5,0),(-3,-2),(2,13),(4,19)}

Solution set = {(-3,-2),(2,13),(4,19)}

Solve Using a Given Domain

Domain = the x’s for your solution setlthat you can use

Substitute the x’s to find their y’s.

Solution set = the set (x,y)’s

Solve 9x+3y=15 if the domain is { 0,1,2,3}

First…solve the equation for y9 3 15x y 9x 9x

3 9 15y x 3 9 153 3y x

3 5y x

Solve 9x+3y=15 if the domain is { 0,1,2,3}

x y=-3x+50

1

y=-3(0)+5y

y=-3(1)+5

= 5

= 2

Solve 9x+3y=15 if D={ 0,1,2,3}

x y=-3x+501

y=-3(0)+5y

y=-3(1)+5= 5= 2

2

y=-3(2)+5 = -13

y=-3(3)+5 = -4

Sol. Set={(0,5),(1,2),(2,-1),(3,-4)|